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On $☆$ - associated comonotone functions

Ondrej Hutník, Jozef Pócs (2018)

Kybernetika

We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to $+$ -associatedness of functions (as proved by Boczek and Kaluszka), but also to their $☆$ -associatedness with $☆$ being an arbitrary strictly...

On asymptotic behaviour of universal fuzzy measures

Ladislav Mišík, János T. Tóth (2006)

Kybernetika

The asymptotic behaviour of universal fuzzy measures is investigated in the present paper. For each universal fuzzy measure a class of fuzzy measures preserving some natural properties is defined by means of convergence with respect to ultrafilters.

On possibilistic marginal problem

Jiřina Vejnarová (2007)

Kybernetika

A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a $T$ -product extension. Finally, a necessary...

On some contributions to quantum structures by fuzzy sets

Beloslav Riečan (2007)

Kybernetika

It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.

On some properties of submeasures on MV-algebras

Mária Jurečková, Ferdinand Chovanec (2004)

Mathematica Slovaca

On the double $g$ -integral.

Markova, Andrea, Riečan, Beloslav (1996)

Novi Sad Journal of Mathematics

On the extension of $D$ -poset valued measures

Beloslav Riečan (1998)

Czechoslovak Mathematical Journal

A variant of Alexandrov theorem is proved stating that a compact, subadditive $D$ -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.

On the $g$ -entropy and its Hudetz correction

Beloslav Riečan (2002)

Kybernetika

The Hudetz correction of the fuzzy entropy is applied to the $g$ -entropy. The new invariant is expressed by the Hudetz correction of fuzzy entropy.

On the individual ergodic theorem in $D$ -posets of fuzzy sets

Beloslav Riečan (2000)

Czechoslovak Mathematical Journal

Calculus for observables in a space of functions from an abstract set to the unit interval is developed and then the individual ergodic theorem is proved.

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

Michał Boczek, Marek Kaluszka (2016)

Kybernetika

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the...

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